Navigation satellite systems (NSS) include both global navigation satellite systems (GNSS) and regional navigation satellite systems (RNSS), such as the Global Positioning System (GPS) (United States), GLONASS (Russia), Galileo (Europe), BeiDou (China), QZSS (Japan), and the Indian Regional Navigational Satellite System (IRNSS) (systems in use or in development). A NSS typically uses a plurality of satellites orbiting the Earth. The plurality of satellites forms a constellation of satellites. A NSS receiver detects a code modulated on an electromagnetic signal broadcast by a satellite. The code is also called a ranging code. Code detection includes comparing the bit sequence modulated on the broadcasted signal with a receiver-side version of the code to be detected. Based on the detection of the time of arrival of the code for each of a series of the satellites, the NSS receiver estimates its position. Positioning includes, but is not limited to, geolocation, i.e. the positioning on the surface of the Earth.
An overview of GPS, GLONASS and Galileo is provided for instance in sections 9, 10 and 11 of reference [A] (a list of references is provided at the end of the present description).
Positioning using NSS signal codes provides a limited accuracy, notably due to the distortion the code is subject to upon transmission through the atmosphere. For instance, the GPS includes the transmission of a coarse/acquisition (C/A) code at about 1575 MHz, the so-called L1 frequency. This code is freely available to the public, whereas the Precise (P) code is reserved for military applications. The accuracy of code-based positioning using the GPS C/A code is approximately 15 meters, when taking into account both the electronic uncertainty associated with the detection of the C/A code (electronic detection of the time of arrival of the pseudorandom code) and other errors including those caused by ionospheric and tropospheric effects, ephemeris errors, satellite clock errors and multipath propagation.
An alternative to positioning based on the detection of a code is positioning based on carrier phase measurements. In this alternative approach or additional approach (ranging codes and carrier phases can be used together for positioning), the carrier phase of the NSS signal transmitted from the NSS satellite is detected, not (or not only) the code modulated on the signal transmitted from the satellite.
The approach based on carrier phase measurements has the potential to provide much greater position precision, i.e. down to centimetre-level or even millimetre-level precision, compared to the code-based approach. The reason may be intuitively understood as follows. The code, such as the GPS C/A code on the L1 band, is much longer than one cycle of the carrier on which the code is modulated. The position resolution may therefore be viewed as greater for carrier phase detection than for code detection.
However, in the process of estimating the position based on carrier phase measurements, the carrier phases are ambiguous by an unknown number of cycles. The phase of a received signal can be determined, but the number of cycles cannot be directly determined in an unambiguous manner. This is the so-called “integer ambiguity problem”, “integer ambiguity resolution problem” or “phase ambiguity resolution problem”, which may be solved to yield the so-called fixed solution.
GNSS observation equations for code observations and for carrier phase observations are for instance provided in reference [A], section 5. An introduction to the GNSS integer ambiguity resolution problem, and its conventional solutions, is provided in reference [A], section 7.2. The skilled person will recognize that the same or similar principles apply to RNSS systems.
The main GNSS observables are therefore the carrier phase and code (pseudorange), the former being much more precise than the latter, but ambiguous. These observables enable a user to obtain the geometric distance from the receiver to the satellite. With known satellite position and satellite clock error, the receiver position can be estimated.
As mentioned above, the GPS includes the transmission of a C/A code at about 1575 MHz, the so-called L1 frequency. More precisely, each GPS satellite transmits continuously using two radio frequencies in the L-band, referred to as L1 and L2, at respective frequencies of 1575.42 MHz and 1227.60 MHz. With the ongoing modernization of the GPS, signals on a third L5 frequency are becoming available. Among the two signals transmitted on L1, one is for civil users and the other is for users authorized by the United States Department of Defense (DoD). Signals are also transmitted on L2, for civil users and DoD-authorized users. Each GPS signal at the L1 and L2 frequency is modulated with a pseudo-random number (PRN) code, and with satellite navigation data. Two different PRN codes are transmitted by each satellite: a C/A code and a P code which is encrypted for DoD-authorized users. Each C/A code is a unique sequence of 1023 bits, which is repeated each millisecond. Other NSS systems also have satellites transmitting multiple signals on multiple carrier frequencies.
Reference [B] relates to processing GNSS data for enhanced real-time kinematic (RTK) positioning. Paragraph [0005] thereof explains that, in traditional RTK positioning, “the rover receiver (rover) collects real-time GNSS signal data and receives correction data from a base station, or a network of reference stations”, but the correction data arrives “at the rover with a finite delay (latency) due to processing and communication”. The delay (latency) problem associated with the correction data is further discussed in reference [B], paragraphs [0006], and [0008] to [0015]. Delta phase methods have been proposed to address that problem (reference [B], paragraphs [0007], and [0036] ff.), by means of a Kalman filter that uses carrier phase increments, called delta phases, to propagate a position solution from a past time to a current time.
There is a constant need for improving the implementation of positioning systems based notably on GNSS (or RNSS) measurements, to obtain a precise estimation of the receiver position, and in particular to quickly obtain a precise estimation, so as to increase the productivity of positioning systems.